Authors: Steven Kenneth Kauffmann
Thirring and Feynman showed that the Einstein equation is simply a partial differential classical field equation, akin to Maxwell's equation, but it and its solutions are required to conform to the GR principles of general covariance and equivalence. It is noted, with examples, that solutions of such equations can contravene required physical principles when they exhibit unphysical boundary conditions. Using the crucially important tensor contraction theorem together with the equivalence principle, it is shown that metric tensors are physical only where all their components, and also those of their inverse matrix, are finite real numbers, and their signature is that of the Minkowski metric. Thus the "horizons" of the empty-space Schwarzschild solution metrics are unphysical, which is traced to the boundary condition that arises from the minimum energetically-allowed radius of a positive effective mass. It is also noted that "comoving" ostensible "coordinate systems" disrupt physical boundary conditions in time via their artificial "composite time" which can't be registered by the clock of any observer because it is "defined" by the clocks of an infinite number of observers. Spurious singularities ensue in such unphysical "coordinates", which fall away on transformation of metric solutions to non-"comoving coordinates".
Comments: 4 Pages. Adapted from a contributed talk at HTGRG-2, 11 August 2015, Quy Nhon, Vietnam.
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